Visual Astronomy at the Telescope's Eyepiece

Mel Bartels

As
a small child I remember being driven back to Portland, Oregon at night
after a visit to relatives in the countryside. I lay in the back of the
station wagon, peering up at the sky through the rear window. The stars
were so brilliant against the darkest black of skies. It hurt my eyes
to look at the brightest stars. What a contrast to the washed out city
skies of Portland, even in 1960.

The Greek astronomer Hipparchus
in the 2nd century BC invented the magnitude system, where the
brightest stars are of 1st magnitude and the dimmest are of 6th
magnitude. I suspect that this system was in use beforehand: it’s
common for humans to divide groups of things into sixes and it would
have been natural for us to call the brightest stars “first class”.

The
magnitude system is logarithmic, not linear. This no doubt because our
eyes work logarithmically (or at least semi-logarithmically). For
example, a star that is 1 magnitude brighter is 250% brighter;
conversely a star that is 0.1 magnitudes dimmer is 10% dimmer.

The
first lesson then is that we cannot get hung up on linear percentages,
instead we must think in logarithmic magnitudes. This is difficult
because discussions today are almost universally in percentages, which
is completely misleading. Illumination drop-off at the edge of the
eyepiece? Stated in percentages (e.g. 15% sounds terrible), should be
in magnitudes (e.g. 0.06 mag, unnoticeable visually). Mirror coating
reflections? Stated in percentages (e.g. 92%) should be in magnitudes
(e.g. 0.04 mag loss). It is very difficult to see differences of 0.2
magnitude or less. And when the view is dimmed, both object and
background are equally dimmed, leaving the contrast unchanged. Unless
the view is grossly dimmed, the unchanging contrast means that the
object does not lose visibility. I will be using magnitudes exclusively
just as
charts and observing manuals.

I've been enthusiastically
observing for a number of decades. Here are the factors that influence
what I can see that night through the eyepiece of my telescope.

• Aperture is the biggest factor. More aperture increases visibility regardless of magnification or power.• Seeing the object in a larger scope then returning immediately to your smaller scope can result in a half magnitude gain.• Observer experience is worth 2 magnitudes (I have a series of sketches of M31 from childhood onward).• Observer variation is a half magnitude or more.• Age matters a magnitude: young kids can see very faint stars; as we get older, our lens yellows and ability to detect fades.• Knowing where to look and what to look for worth a magnitude.• Averted vision is worth a magnitude.• Dark adaption continues to produce increasing benefits for hours, ultimately worth maybe a half a magnitude.• Field baffling is an overwhelming factor: the difference between nonexistent and fully baffled views can be worth magnitudes.• Covering your head with a black cloth also yields improvements, perhaps on the order of a fraction of a magnitude.•
Time at the eyepiece is worth a magnitude (objects gradually become
recognizable or detectable over a period of time, and then they fade
after a prolonged period of continuous observing).• Comfort at the eyepiece is worth a half magnitude.•
Rested eyes are worth half a magnitude. I often take short breaks
throughout the night. Upon returning to the eyepiece I can see more
until my eyes tire.• Sky transparency is such an overwhelming
factor; on rare perfect nights I’ve seen scopes perform as if they had
almost unlimited aperture; let’s call superb sky transparency worth a
magnitude or two.• Filters are worth a magnitude.• Visibility
appears to correlate most with aperture, then apparent size (the
greater the aperture, the greater the apparent size, limited by the
full field of view).• True binocular or two eyed viewing results in
a half magnitude gain in stellar limiting magnitude and about a
magnitude gain for extended objects.

Make these factors work for you and you can gain magnitudes in observing prowess. It’s like having a much larger scope on hand.

Why
do amateurs ignore these factors in favor of obsessing over minutia
like their telescope’s diagonal coating quality? Sometimes we humans
become superstitious and engage in myopic inquisitions when the
situation is difficult or fuzzy. Have courage, don’t obsess over some
detail of your telescope and instead focus on the factors that matter.

Given
a reasonable mix of these factors, how faint can you expect to see? The
following chart is based on my decades of observing experience using
scopes up to 40 inches [1M] in size.

Notice
that the lines are banded or thickened. You might fall slightly above
or below these bands based on the factors discussed earlier.
Beware of anyone or any calculator that states overly precise limiting
magnitudes. These are at best guides and give a false impression that
an object is either perfectly visible or perfectly invisible. Objects
on the edge of visibility come in and out of view over a period of
time. One night that object might be visible three times in a half hour
(my standard for detectability). On another night it simply is
completely invisible. On rare perfect nights not only can I detect it
much of the time but there is detail too. Also if
the galaxy or cluster or planetary is unusually large, then the
detection limit
will suffer. Note that as aperture increases, minor differences (say
between a 20 inch and a 22 inch telescope) become insignificant, even
undetectable except for rare edge cases.

At
first aperture is everything, then it is nothing; eventually it simply
is. At first we can't get enough aperture. Then almost like a boomerang
we trim way back in aperture. Notice how many experienced amateurs own
not only their big scope but also a smaller scope? Finally, aperture
takes its place in the pantheon of factors, being traded for field of
view and for convenience of viewing. A 6 inch [15cm] is a
perfect aperture to learn how to observe. With it you can see thousands
of objects from a dark sky.
A 12 inch [30cm] will resolve almost all clusters and show galaxy
groupings.
If you think that you “need” large aperture to see the
skies, that small aperture won’t work, then something has seriously
gone amiss. Large aperture makes it more difficult to learn the art of
observing. Do yourself a favor and spend a lot of time observing with
smaller scopes too.

What magnifications should be used? I favor three strategies both based
on exit pupil (the eyepiece's focal length in mm divided by the
telescope's overall focal ratio [e.g., 24mm eyepiece on a F/6 scope
produces a 4mm exit pupil]):

The first is based on Richard Berry's advice. Arrange your eyepieces so that they give exit pupils as following:
5-7mm Richest Field observing
3-5mm best deep sky observing
1-2mm best detailed observing (globulars, planetaries, lunar and planetary)

The
second is based on Stephen O'Meara's comments (e.g., his Herschel 400
Observing Guide). He uses modest aperture (4 inches [10cm]) at low,
medium and high powers. He takes his time studying the object carefully
at each power. His low, medium and high exit pupils are:4.4mm1.4mm0.96mmIf
you are wondering who to look to for observing advice, pay attention to
the top observers who use smaller scopes, like O'Meara.

The third is a strategy that I've
developed in response to the super wide angle eyepieces available
today. It allows me to see large scale objects otherwise too big for a
given scope. I call this strategy “framing” or
“composing”
the view where the object is magnified to fill the eyepiece’s field of
view
as much as possible with a nice border around it for contrast.
Increasing the apparent object size
beyond this 'cut-off' results in a less pleasing more difficult view.
Here, the
widest possible field of view is important, even at the cost of more
glass for the light to pass through. In this approach, I smoothly
decrement the exit pupil. I use a set of exit pupils as
follows (note that the typical set of eyepieces does not fit
nicely):5-6mm for largest scale objects3-4mm for medium scale objects1-2mm for small scale objects

It helps to have an observing program and plan your evening's viewing. The Astronomical League has a number of observing plans.
Or create your own, i.e., comparing the shapes of globular clusters in
the Sagittarius region or colorful double stars in Bootes. Use a table
for your eyepieces, tools, charts and texts or for your tablet
and lightshield. Plan on 20 minutes per object. I strongly encourage
you to sketch what you see. This hones your observing skills and brings
out details in the object. Observe at all three ranges of power: low,
medium and high.

Averted vision works best if you know where to aim your eyes
in the field of view. Here's a chart to help.

For extended objects, things are not as simple as stars. For
starters,
it is not possible to increase the surface brightness of an extended
object by increasing the aperture. An example: take an object of 10
magnitude/ square arcsecond as seen by the unaided eye at night, exit
pupil open to 7mm. Now, look at the object through a 10" scope. If
there is no magnification to the image, the surface brightness will
increase by the ratio of the scope's aperture to the eye's aperture
squared, or, (10"/0.3")^2 =~ 1000x. However, in order to fit all of the
light from the 10" aperture into the eye's exit pupil, we must use at
least 33x. 33x will dilute the image brightness by 33^2 =~ 1000x, so we
are back where we started. In fact, because of mirror coatings not
reflecting 100%, and the small obstruction caused by a diagonal, the
image brightness per area will actually be a little less than with the
unaided-eye.

This leads to the
interesting conclusion that the brightness of the sky glow as seen in the
eyepiece is entirely dependent on exit pupil. At a given
location on a given night, no matter the size of scopes, if they are
giving the same exit pupil, then the sky glow brightness will be
very similar.

So why then is aperture the dominant factor? If exit pupil
or sky background brightness is kept constant, then as aperture increases so
must the magnification. The object appears larger and is easier to see. It’s
like moving in closer. If magnification is kept constant then the object and
background brightness increase, also making the object easier to see.

What is sky glow brightness? The night sky,
even at very dark sites, glows faintly due to zodiacal light and
airglow. See Brian Skiff's discussion at http://www.astropix.com/HTML/L_STORY/SKYBRITE.HTM.
You can measure the darkness (or brightness) of your night using a sky
glow meter available at http://unihedron.com/projects/darksky/.
Dark sky sites have readings close to 21.5 magnitudes per square
arcsecond. Observing through a telescope with your eye's pupil fully
opened results in a sky glow in the field of view equal to
that of the night sky. Magnifying the image results in smaller exit
pupils, the useful maximum magnification or smallest exit pupil being
close to 1mm. The sky glow brightness drops more than 4
magnitudes to close to 26 magnitude as exit pupil shrinks to 1mm.

There's a great deal of discussion about Blackwell's studies and Clark's presentation. Here's my take:

So how can we see the object in the
scope? The eye is a marvelous detector of low contrast faint objects,
but the light must fall on large numbers of rod cells so that the
eye-brain can detect the slight contrast difference between object and
background. The slighter the contrast, the more rod cells that the
object's light must fall on in order to generate a signal difference
between object and background. By increasing the telescope
magnification, the object is magnified so that its light falls on many
rod cells. There are two points to consider when an object is in the
field of view of an eyepiece. The first is the object combined with the
sky glow from the atmosphere that is directly between us and the
object, and the second is a point away from the object, which is the
sky glow only. The ratio of brightness between these two points is
sometimes called the object contrast. This contrast value stays
constant despite any
increase in magnification because both points are equally dimmed.

The seminal reference on visual astronomy is Clark's book, "Visual
Astronomy of the Deep Sky". In it Clark explains and quantifies the visual detection of objects. Clark has added additional comments since the
book's publication, at http://clarkvision.com/visastro/omva1/index.html Clark uses data from a World War II study by Blackwell.

Here a brief presentation of the Blackwell data. The eye's detection ability with sky background brightness
values from 21 to 26 is:

From
the chart we can see that large exit pupils result in the best ability
to detect objects over a wide range of apparent sizes. As the exit
pupil shrinks, the ability to detect objects declines and becomes
concentrated on apparent sizes of about a degree. We can see this by
plotting best apparent detection size against declining sky background
brightness. Here are two visualizations of the data:

The data and its interpretation has been the subject of intensive
discussions between Prof Clark, Nils Olaf Carlin, Harold Lang and
myself.

For Nils Olof Carlin's analysis of Blackwell's
original data, see blackwel.html.
Here, Nils shows that the best contrast comes when the background is
dimmed below visual detection and the object is about one degree in
apparent size.

I wrote a visual detection calculator
that presents the data by aperture and exit pupil. I believe that the
whole issue of visual detection needs more observations and possibly a
new model. The detector that I wrote uses the Blackwell data. Like any
ground breaking study, there remains much to be done. The study was
done with two eyes - how does a single eye do? Objects in with complex
isophotes need to be studied, distractions of other objects
in the field of view needs to be investigated and variations in the
color of the objects need to be checked. Also needing observations is
variation in the ages of the observers and especially telescope
construction features like baffling and cleanliness of optics.

Greg
Crinklaw has invested a great deal of time into improving his visual
detection calculator based on empirical results at the eyepiece. See
his SkyTools software and in particular his comet chasing page.